Average calculation discrepancies between two different approach

1

Hi all,

I tried to calculate the volume average but the results are different for the two methods.

assemble(sol[1]*dx)/assemble(Constant(1)*dx)

sol[1].vector().sum()/mesh.num_cells()

From what I understand, these two should yield the same results.

Thanks.

2

In your second average, you are using number of cells, where you should use the length of the vector you are summing over, i.e.

from dolfin import *


def average(N):
    mesh = UnitIntervalMesh(N)
    V = FunctionSpace(mesh, "CG", 1)
    x = SpatialCoordinate(mesh)
    u = project(x[0], V)
    dx = Measure("dx", domain=mesh)
    print(N, assemble(u*dx)/ assemble(Constant(1)*dx), u.vector().sum()/len(u.vector()))

for n in [3, 10, 20, 40, 80]:
    average(n)

yielding:

3 0.5 0.5
10 0.5 0.5000000000000001
20 0.5000000000000001 0.5000000000000002
40 0.5000000000000001 0.5
80 0.5000000000000001 0.5000000000000001